Asoftball thrown into the air has a parabolic trajectory. after reaching a maximum height of 28 feet, the ball covers a ground distance of 4 feet before hitting the ground. which equation describes the ball’s trajectory?

Step-by-step explanation:

A softball thrown follows a parabolic path.

We are given that the maximum height is 28 feet

So, The y coordinate of vertex is 28 i.e. k = 28

Now we are given that the ball covers a ground distance of 4 feet before hitting the ground.

So, x intercept is 4 feet

Initially the height of the ball is 0 i.e. y = 0 and the distance traveled by the ball along x axis is also 0

So, points on the parabola are (0,0) and (4,0) (Refer the attached figure)

So, the x coordinate of vertex is the x coordinate of mid point of (0,0) and (4,0)

So, the x coordinate of vertex is 2 i.e. h = 2

So, vertex (h,k)=(2,28)

General form of equation of parabola  :

Substitute the vertex

--A

Since (0,0) satisfies the parabola.

So, substitute (0,0) in A to get value of a

Substitute the value of a in A

Hence the equation describes the ball’s trajectory is

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step-by-step explanation: